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On normal structure, fixed-point property and contractions of type $ (\gamma)$

Author: M. A. Khamsi
Journal: Proc. Amer. Math. Soc. 106 (1989), 995-1001
MSC: Primary 46B20; Secondary 47H10
MathSciNet review: 960647
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Abstract: We prove that a Banach space $ X$ has normal structure provided it contains a finite codimensional subspace $ Y$ such that all spreading models for $ Y$ have normal structure. We show that a Banach space $ X$ is strictly convex if the set of fixed points of any nonexpansive map defined in any convex subset $ C \subset X$ is convex and give a sufficient condition for uniform convexity of a space in terms of nonexpansive map of type $ \left( \gamma \right)$.

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Keywords: Nonexpansive mappings, normal structure, fixed point property
Article copyright: © Copyright 1989 American Mathematical Society

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